| The dissertation studies the reconstruction of vibroacoustic responses of an elastic structure using Helmholtz Equation Least Squares (HELS) method in three-dimensional space based on the measurement of field acoustic pressures on a hologram surface very close to the source structure. In HELS method, the acoustic pressure is expressed in a series expansion of localized spherical wave functions, the corresponding coefficients are determined by matching the assumed-form solution to the measured acoustic pressures, and the errors are minimized in the least squares sense. Once the coefficients are specified, the acoustic pressures on the arbitrary source surface can then be reconstructed.;The focus of this study was on the reconstruction of the vector acoustic quantities based on the measured field acoustic pressures. Euler's equation was employed in HELS to establish the correlation between the acoustic pressures and the particle velocities. Tikhonov regularization associated with singular value decomposition (SVD) was utilized to ensure the stability of the vector velocity reconstruction. Validations of the reconstructed normal surface velocities were carried out numerically and experimentally for a plate type structure, a highly non-spherical object, and challenging source geometry for HELS method.;Results showed that the success of reconstruction of vibroacoustic responses highly relies on the choice of reconstruction parameters, which include the origin location of the coordinate system, standoff distance from the hologram surface to the source surface, number of measurements, microphone spacing and the ratio of size of measurement aperture to the source area under reconstruction. The interrelationship among those parameters, acoustic wavelength and the characteristic dimension of source geometry were investigated.;To gain insightful information of vibroacoustic responses, SVD was used to decompose the reconstructed surface normal velocities into mutually orthonormal components. Next, the radiation and vibration efficiencies of those orthogonal components were calculated, which enables one to identify the components that are responsible for sound, and those responsible for structural vibrations. The main conclusion of the thesis is that HELS can be utilized to reconstruct vibroacoustic responses and to yield insightful information on the root causes of sound radiation from a vibrating structure. |
